# Surface Area of a Hexagonal Pyramid

The surface area, or total surface area (TSA), of a hexagonal pyramid, is the entire space occupied by its seven faces. It is measured in square units such as m2, cm2, mm2, and in2.

## Formula

The formula is given below:

The formula to calculate the surface area of a hexagonal pyramid also includes its lateral surface area (LSA).

Lateral Surface Area (LSA) = 3bs, here b = base, s = slant height

Total Surface Area (TSA) = 3ab + LSA

Let us solve some examples to understand the concept better.

## Solved Examples

Find the lateral and total surface areas of a hexagonal pyramid with a base of 5 cm, an apothem of 4.33 cm, and a slant height of 9 cm.

Solution:

As we know,
Lateral Surface Area (LSA) = 3bs, here b = 5 cm, s = 9 cm
LSA = 3 × 5 × 9
= 135 cm2
Total Surface Area (TSA) = 3ab + LSA, here a = 4.33 cm, b = 5 cm, LSA = 135 cm2
TSA = 3 × 4.33 × 5 + 135
= 199.95 cm2

Finding the surface area of a hexagonal pyramid when the BASE and HEIGHT are known

Find the surface area of a hexagonal pyramid with a base of 4 cm, and a height of 6 cm.

Solution:

We will use an alternative formula for finding the surface area of a hexagonal pyramid.
Total Surface Area (TSA) = ${\dfrac{3\sqrt{3}}{2}b^{2}+3b\sqrt{h^{2}+\dfrac{3b^{2}}{4}}}$, here b = 4 cm, h = 6 cm
TSA = ${\dfrac{3\sqrt{3}}{2}\times 4^{2}+3\times 4\times \sqrt{6^{2}+\dfrac{3\times 4^{2}}{4}}}$
= 124.71 cm2